Q.Will Cutting Back Sunshine Ligustrum Save Plants From Way Too Much Rain This Winter In Mississippi
My plants are two years old. They have lost most of their leaves. Mississippi has had record amount of rain this winter. Drainage does not seem to be the problem
– we have just had too much rain. My whole yard is very wet and has been for several months.

Certified GKH Gardening Expert
No, it will not save the shrubs to prune, alone.
If you treat for a fungal infection before you cut them, and make sure to dispose of all of the infected growth removed, then you can expect to see the shrub's health return.
These articles will help:
https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm
https://www.gardeningknowhow.com/plant-problems/disease/using-lime-sulfur-in-gardens.htm
https://www.gardeningknowhow.com/ornamental/shrubs/ligustrum/pruning-privet-hedges.htm
https://www.gardeningknowhow.com/ornamental/shrubs/ligustrum/growing-ligustrum-shrubs.htm